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no the amount of existing trade routes has no impact on the success of trade missions.
The only important factors are the character's intelligence, the bargaining bonus (this is a family value, so an average of all members' attributes) and their remaining life (if their time comes to an end during their trip, they will die the same they would if they were at home). But there is still a (small) element of luck.
You can always make sure the character wears items to boost their intelligence and bargaining bonus, maybe charisma, too).
Each destination has their own value to compete with, so sensing one family member after they failed previously, is probably not going to give you a better result unless they increased their stats in the mean time.
From what you said
"Each destination has their own value to compete with, so sensing one family member after they failed previously, is probably not going to give you a better result unless they increased their stats in the mean time. "
If I send them out without any changes I should always get the same result.
In my current game. I sent the wife to open a trade route. Then I forgot to pause and go do something. When I return, the wife return to the port with success mission. But the husband standing there doing nothing, since I didn't put auto mode on him.
I load back to the time wife is running to port to open trade route. Then I play normally. When the wife return, now the mission fail.
Both cases got nothing changes at all since the husband didn't gain enough experience to level up.
Your character's stats increase the odds, but there will always be an element of chance. If your character had a 90% chance of success, there is still a 10% chance of failure. At the same time, your character could have been very lucky in the first try, even though they might have had a very low chance of success.
But luck aside, it is always the safer choice to focus on the stats and make sure you increase them before trying again.
Thank you very much.
Commoners Clothes: +10 armor, +2 stealth, +3 resistance: Chance 53%
Garb of Arrogance: +4 resistance, +5% ability to gain influence, +5% ability to learn, +4% reputation bonus: Chance 53%
Gorgeous Clothes: +5 resistance, +10 bonus when bargaining, +3 intimidation: Chance 50%
Note that when you select a destination, you see on the left "Intelligence" and "Bonus when bargaining". On the right you see "Intimidation (" + character_name + ")"
It seems to me that Intimidation is a negation to this chance and Bonus when Bargaining is suppose to increase this chance but has very little effect. I then added the money bags on top of the Garb of Arrogance and it raised my chance from 53% to 54% though the Bonus was increased only +2. After all the messing around with these tests I realized I was wielding a gun that added intimidation so I removed it before setting off on my journey. This raised my overall chances another 3%. Note that certain professions add intimidation as well. Grave Digger for instance.
Next I removed the money bags, restoring me to 53% and added a Diamond (+1 Charisma, +3 Reputation bonus). This actually dropped my chance down to 52% (Garb of Arrogance). Without the diamond my Bonus with bargaining was 2. With the diamond it was 2.25 so while it went up, my chances dropped, which seems like a bug. The Free Citizens Garb (+8 Bonus when bargaining) did seem to give me a significant enough boost to mention (increased chance by another +4% over the Garb of Arrogance).
Next, I used an About Talents II book to increase intelligence by +2 for a little while. This raised my odds a whopping +10% (amounting to 63%) but the duration of this effect may expire before a mission completes. I'm not sure but the chance of success might be recalculated when he returns.
With Talents II in effect, you can't use another one so I tried About Talents I to add +1 intelligence. This raised the chance of success to 66% or +3% with just one more intelligence point. So it would seem adding more intelligence has a decreasing affect.
Being "scented" with Dartagnan's fragrance does not seem to raise Charisma. Perfume does raise it by +1 but this had no impact on my chances yet. Adding on the use of Flannel also increased Charisma by +1 but the increased charisma resulted in a decrease in chance. While the bonus when bargaining was up from the increased Charisma, it seems it has varied implications.
If you unlock Patrician, you can buy the Social Skills "Enchanting 1" (+1 Charisma) and "Business Sense 1" (+2 Intelligence) for added boosts. There are even more as you climb the political ladder.
The mission takes 6 hours from when your character leaves the map so place him just outside of the trade route exit point before you use any of the books to increase your odds.
About testing with game saves. If you save just before your mission ends, you likely will not change the outcome by reloading if it fails. I tried this at the 53% success chance to save money and after 8 reload attempts, I still could not succeed. This would indicate the success chance is determined when you depart.
Lastly, I have determined that while away, if you had a pending candidacy for a city office, you can still win. I was competing against several others in this office and still won while away.